Plato's Phaedo makes a lot of interesting arguments that are well worth the time taken to contemplate them.  Some of the principle arguments will be dealt with here by providing a brief account of their structure, and examining their validity and truth value, as seen by Plato and scholars of Plato.

The suicide argument that Socrates offers early in the text is roughly made in the following form:

Premise 1: Death is the separation of soul from body.

Premise 2: The philosopher acting as a philosopher, seeks to affect this separation as far as possible.

Conclusion: Therefore, the philosopher practices death.

This is an argument that Socrates makes to illustrate why he in unafraid of dying, and why he is thinking rationally when he lacks this fear.  Two thoughts to think about are that it is a problem for Plato and Socrates if you say the person dies, and the soul makes up the person because then the soul dies.  Remember, that Plato is using Socrates to show that the soul is immortal so this objection is certainly a problem that must be considered by scholars of the text.

Another slight problem comes when Socrates advocates learning with the mind alone, which necessarily implies learning without the body or senses.  But does Plato truly mean that we can and should learn without the senses? It would most likely be terribly difficult to acquire skills requisite to knowledge if we could make no use of our senses.  This is the position that a lot of empiricists (another type of philosophy in contrast to rationalists) take on matters of knowledge and learning.

There are parts of this text when Plato speaks about the sensibles and the form of properties.  His goal in such a discussion is to show that the sensibles are not the same things as the Forms.  An example of the sensibles would be things in the world like horses, men, books, and mountains.  They are what we perceive with our senses, and according to Plato they are inferior to the Forms.  The intangible, divine, perfect ideals of Beauty, Good, Truth and the like are examples of the Forms.  Plato believes that knowledge of everything lies in the Forms and that they are necessary causes of all sensibles.  The Forms are a sort of realm like heaven for Plato, where we commune with them as souls learning and doing the dialectic.  Socrates often draws analogies between the Forms and the soul in Platonic dialogues.  Plato wants to show that both the Forms and souls are indivisible and indestructible, but there are points in his texts when this becomes a very difficult task. 

The immortality argument for the soul is outlined as follows:

1) opposites cannot admit of their opposites (when opposed they either flee or perish)

2) carriers cannot admit the opposite of what they carry

3) the soul is a carrier; what it carries is life

4) the opposite of life is death

5) the soul can't admit of death; it must either flee or perish

6) the soul is therefore deathless

7) what is deathless is indestructible

8) the soul is indestructible (i.e. immortal)

There is a fallacy in this argument though that is that it doesn't follow from the soul make whatever it is in alive to that the soul itself is alive.  This is of course that a philosopher like Plato ought to address, but his argument for the immortality of the soul is otherwise quite impressive as Socrates presents it.

And finally an important point to note about the Phaedo is the grace with which Socrates faces his final hours.  This work is quite a testimony to the character of Socrates, as Plato saw from his perspective, and an inspiration to those who truly believe in themselves and their personal philosophy.  Socrates was a dedicated philosopher with a talent for discussion and a passion for learning.  He was remembered by his friends for being wise and good-natured, and in the closing words of Phaedo, "such was the end of our comrade.a man who we would say, was of all those we have known the best, and also the wisest and the most upright."